If a sample originally had 120 atoms of carbon-14, how many atoms will remain after 16,110 years?
We know that carbon-14 (
The half-life with respect to the rate constant would be found to be:
#t_"1/2" = (ln2)/(k)#
where the point of showing the equation is that it does not depend on the concentration of
#""^14 "C"#, which is what a zero-order process is.
Logically, what happens in a half-life decay is that half the sample becomes something else, so of course, when we focus on the original sample, we would see that half is left when the process has occurred once.
After each half-life passes by, we lose half of the remaining sample, so you can see that we can simply halve the concentration
It therefore makes sense that after
#color(blue)([""^14 "C"]_f = 1/(2^n)[""^14 "C"]_i)#
Using the half-life of carbon-14, which is known to be about
#= 1/(2^("16110/5730"))[""^14 "C"]_i#
We would actually see that this gives the final concentration of